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Dynamical Coupled Channel Approach for Meson Production Reaction

Dynamical Coupled Channel Approach for Meson Production Reaction. T. Sato Osaka U./KEK . contents. Motivation Analysis of meson production reaction and dynamical coupled channel model extracting resonance parameters Resonance mass and width Role of reaction dynamics on resonance properties

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Dynamical Coupled Channel Approach for Meson Production Reaction

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  1. Dynamical Coupled Channel Approach for Meson Production Reaction T. Sato Osaka U./KEK contents • Motivation • Analysis of meson production reaction and dynamical coupled channel model • extracting resonance parameters • Resonance mass and width • Role of reaction dynamics on resonance properties • N* and neutrino reaction • Summary

  2. motivation Q: Why we investigate N*, what is key N* quantity? A1 masses and coupling constants are fundamental quantity that characterize low energy hadron physics well defined resonance parameters: pole(mass) and residue(coupling constants) A2 reveal how QCD is realized in low energy hadron physics In practice, we test spectrum, form factors predicted from effective theory of QCD nature of excited baryon can be significantlyaffected by the reaction dynamics

  3. to proceed • Determine high precision partial wave amplitude F(W) from accurate and complete experiments • data are incomplete and have errors • Extract resonance poles and residues from F(W) for complex W by using analytic continuation of F(W) • analytic continuation can be done within known analytic structure • of each approaches • Our dynamical coupled channel approach • reduce errors in extracting nucleon resonances by interpolating • data by using dynamical reaction model • implement essential element of non-perturbative QCD as much as we can • extract resonance pole,residue • provide interpretations of the extracted resonance parameters

  4. Analysis of meson production reaction and dynamical coupled-channels (DCC) model

  5. Dynamical coupled-channels (DCC) model for meson production reactions Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) start from Hamiltonian of meson-baryon system Excited baryon continuum interaction  Solve scattering equation(3dim) that satisfies three-body unitarity Meson cloud Confined core

  6. coupled-channels effect t-channel contact u-channel s-channel p, r, s, w,.. N N, D p D p r,s N p N D D p coupled-channels effect N*bare

  7. Dynamical Coupled-Channels analysis Fully combinedanalysis of gN , N  N , hN , KL, KSreactions !! 2010-2012 8channels (gN,pN,hN,pD,rN,sN,KL,KS) < 2.1 GeV < 2 GeV < 2 GeV < 2 GeV < 2.2 GeV < 2.2 GeV 2006-2009 6channels (gN,pN,hN,pD,rN,sN) < 2 GeV < 1.6 GeV < 2 GeV ― ― ― • # of coupled channels • p  N • gp N • -p hn • gphp • ppKL, KS • gpKL,KS Kamano, Nakamura, Lee, Sato, 2012

  8. Partial wave amplitudes of pi N scattering Real part preliminary Kamano, Nakamura, Lee, Sato, 2012 Previous model (fitted to pN  pN dataonly) [PRC76 065201 (2007)] Imaginary part

  9. KY production reactions Kamano, Nakamura, Lee, Sato, 2012 preliminary 1757 MeV 1792 MeV 1732 MeV 1879 MeV 1845 MeV 1879 MeV 1966 MeV 1985 MeV 1966 MeV 2031 MeV 2059 MeV 2059 MeV

  10. Kamano, Nakamura, Lee, Sato, 2012

  11. Extracting resonance parameters

  12. Method of analytic continuation Suzuki, Sato, Lee, Phys. Rev. C79, 025205 (2009) Phys. Rev. C 82, 045206 (2010) deform the path of momentum integral for complex E find pole of T-matrix choosing appropriate sheets for each channels On-shell momentum Singularity of meson exchange interaction

  13. Mass, width and form factors of resonances A1 masses and coupling constants are fundamental quantity that characterize low energy hadron physics

  14. Spectrum of N* resonances Kamano, Nakamura, Lee, Sato ,2012 Real parts of N* pole values preliminary Ours PDG 4* PDG 3* L2I 2J

  15. Width of N* resonances preliminary Kamano, Nakamura, Lee, Sato 2012

  16. Form factors(complex numbers) are derived from the residue of the amplitude at resonance pole. Identified with exact solution of fundamental theory (QCD) N-N* form factors at Resonance poles Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010) Suzuki, Sato, Lee, PRC82 045206 (2010) Nucleon - 1st D13 e.m. transition form factors Real part Imaginary part

  17. Role of reaction dynamics on resonance properties ‘A2 reveal how QCD is realized in low energy hadron physics’

  18. Resonance in coupled channel reaction Interesting example on the number of resonances in coupled channel reaction suppose a excited baryon couples with two meson-baryon channel oneobtains poles on several sheets(uu,up,pu,pp) usually, only one pole on nearest sheet from physical sheet is relevant . That is used to characterize resonance In some case, more than one poles become relevant and they can be seen as resonances B1 B2 M1 M2

  19. Toy model: Suzuki,Sato,Lee PRC79 025205(2009) 1 physical 2 physicalsheet threshold 2 threshold 1 Im (E) Re (E) A B 1unphysical2 physicalsheet 1 unphysical 2 unphysicalsheet Single excited state(bare) couples with two continuum channels  Two poles are generated on up(narrow) and uu(broad) sheet can be observed as resonances

  20. Pole positions of P11 Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010) hN threshold pD threshold 1357 – 76 i 1364 – 105 i Im E (MeV) 1820 – 248 i 1999 – 321 i 3 resonance pole out of 2 excited(bare) N* (6-channel model) mass shift of excited states from coupling with scattering state

  21. Interpretation of form factor

  22. GM(Q2) for g N  D (1232) transition Note: Most of the available static hadron models give GM(Q2) close to “Bare” form factor. Full Bare

  23. g p  Roper e.m. transition “Bare” form factor determined from our DCC analysis (2010). “Static” form factor from DSE-model calculation. (C. Roberts et al, 2011)

  24. Collaborators J. Durand (Saclay) B. Julia-Diaz (Barcelona) H. Kamano (RCNP,JLab) T.-S. H. Lee (ANL,JLab) A. Matsuyama(Shizuoka) S. Nakamura (YITP,Kyoto,JLab) B. Saghai (Saclay) T. Sato (Osaka) C. Smith (Virginia, Jlab) N. Suzuki (Osaka) K. Tsushima (Adelaide,JLab)

  25. Toward construction of unified model of lepton-nucleus interaction from a few hundred MeV to GeV region Y. Hayato(ICRR, U. of Tokyo), M. Hirai(Tokyo Science U.),H. Kamano(RCNP,Osaka U.),S. Kumano(KEK),S. Nakamura(YITP,Kyoto U.),K. Saio(Tokyo Science U.),T. Sato(Osaka U.),M. Sakuda(Okayama U.)  A new collaboration at J-PARC branch of KEK theory Center http://j-parc-th.kek.jp/html/English/e-index.html

  26. Lepton-nucleus interactions in the new era of large q13 spring 2012: theta_13 from Daya Bay, RENO mass hirarchyand CP-phase d.

  27. Less than 10% accuracy of the neutrino cross sections is • required for the determination of mass hirarchyand CP-phase d. • Neutrino experiments probe overlapping region among • Quasi-elastic(QE), Resonance(RES), and Deep-inelastic scattering (DIS). DIS QE RES Atmospheric T2K

  28. Neutrino reaction in resonance region W<2GeV • Reaction model for the delta(1232) region is available • Sato,Uno,Lee PRC67(2003) CC • Matsui,Sato,Lee PRC72(2005) NC, PV(e,e’) available neutrino reaction data are explained

  29. Above Delta region, only single pion production reaction has been studied Rein SehgalAP133(80) Alvarez-Ruso et al. PRC57(98) Lin et al. PRC52(95) Paschos et al. PRD65(02) Lalakulich et al. PRD71(05), PRD74(06) Leitner et al. PRC79(09) + non-resonance Hernandez et al. PRD76 (07),PRD81(10) Lalakulich et al. arXiv 1007.0925 Opportunity to apply development of meson production reaction for neutrino reactions

  30. Forward neutrino induced meson production reaction in nucleon resonance region : the first application of coupled channel approach Objective: * benchmark for the future full meson production model * eta,kaon production rate for back ground estimation of proton decay analysis Use PCAC for , Tot (including 2pi) single pi SL model (single pi via Delta) eta K

  31. Next Tasks By extending the ANL-Osaka collaboration (since 1996) Complete the extraction of resonance parameters including N-N* form factors Analysis on the structure of major resonances(S11,D13) 3. Make predictions for J-PARC projects on πΝ -> ππΝ, ΚΛ… 4. Complete model of weak meson production reaction

  32. Kamano, Nakamura, Lee, Sato, 2012

  33. Kamano, Nakamura, Lee, Sato, 2012

  34. Angular distribution Photon asymmetry Single pion photoproduction Kamano, Nakamura, Lee, Sato, 2012 1137 MeV 1137 MeV 1232 MeV 1232 MeV 1334 MeV 1334 MeV 1462 MeV 1462 MeV 1527 MeV 1527 MeV 1617 MeV 1617 MeV 1729 MeV 1729 MeV 1834 MeV 1834 MeV 1958 MeV 1958 MeV Previous model (fitted to gN  pN data up to 1.6 GeV) [PRC77 045205 (2008)] Kamano, Nakamura, Lee, Sato, 2012

  35. Electromagnetic Helicity Amplitude

  36. Analysis Database Pion-induced reactions (purely strong reactions) SAID ~ 28,000 data points to fit Photo- production reactions

  37. Parameters : 1. Bare mass M 2. Bare vertex N* -> MB (C , Λ ) N = 14 [ (1 + 8 2 ) n ], n = 1 or 2 = about 200 Determined by χ -fit to about 28,000 data points N* N*,MB N*,MB N* N* 2

  38. gN D(1232) form factors compared with Lattice QCD data (2006) DCC

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